In this paper, we propose a framework for automatic classification of patients from multimodal genetic and brain imaging data by optimally combining them. Additive models with unadapted penalties (such as the classical group lasso penalty or $L_1$-multiple kernel learning) treat all modalities in the same manner and can result in undesirable elimination of specific modalities when their contributions are unbalanced. To overcome this limitation, we introduce a multilevel model that combines imaging and genetics and that considers joint effects between these two modalities for diagnosis prediction. Furthermore, we propose a framework allowing to combine several penalties taking into account the structure of the different types of data, such as a group lasso penalty over the genetic modality and a $L_2$-penalty on imaging modalities. Finally , we propose a fast optimization algorithm, based on a proximal gradient method. The model has been evaluated on genetic (single nucleotide polymorphisms-SNP) and imaging (anatomical MRI measures) data from the ADNI database, and compared to additive models. It exhibits good performances in AD diagnosis; and at the same time, reveals relationships between genes, brain regions and the disease status.

As a popular tool for producing meaningful and interpretable models, large-scale sparse learning works efficiently when the underlying structures are indeed or close to sparse. However, naively applying the existing regularization methods can result in misleading outcomes due to model misspecification. In particular, the direct sparsity assumption on coefficient vectors has been questioned in real applications. Therefore, we consider nonsparse learning with the conditional sparsity structure that the coefficient vector becomes sparse after taking out the impacts of certain unobservable latent variables. A new methodology of nonsparse learning with latent variables (NSL) is proposed to simultaneously recover the significant observable predictors and latent factors as well as their effects. We explore a common latent family incorporating population principal components and derive the convergence rates of both sample principal components and their score vectors that hold for a wide class of distributions. With the properly estimated latent variables, properties including model selection consistency and oracle inequalities under various prediction and estimation losses are established for the proposed methodology. Our new methodology and results are evidenced by simulation and real data examples.

Principal Components Regression (PCR) is a traditional tool for dimension reduction in linear regression that has been both criticized and defended. One concern about PCR is that obtaining the leading principal components tends to be computationally demanding for large data sets. While random projections do not possess the optimality properties of the leading principal subspace, they are computationally appealing and hence have become increasingly popular in recent years. In this paper, we present an analysis showing that for random projections satisfying a Johnson-Lindenstrauss embedding property, the prediction error in subsequent regression is close to that of PCR, at the expense of requiring a slightly large number of random projections than principal components. Column sub-sampling constitutes an even cheaper way of randomized dimension reduction outside the class of Johnson-Lindenstrauss transforms. We provide numerical results based on synthetic and real data as well as basic theory revealing differences and commonalities in terms of statistical performance.

This paper introduces a fast, general method for dictionary-free parameter estimation in quantitative magnetic resonance imaging (QMRI) via regression with kernels (PERK). PERK first uses prior distributions and the nonlinear MR signal model to simulate many parameter-measurement pairs. Inspired by machine learning, PERK then takes these parameter-measurement pairs as labeled training points and learns from them a nonlinear regression function using kernel functions and convex optimization. PERK admits a simple implementation as per-voxel nonlinear lifting of MRI measurements followed by linear minimum mean-squared error regression. We demonstrate PERK for $T_1,T_2$ estimation, a well-studied application where it is simple to compare PERK estimates against dictionary-based grid search estimates. Numerical simulations as well as single-slice phantom and in vivo experiments demonstrate that PERK and grid search produce comparable $T_1,T_2$ estimates in white and gray matter, but PERK is consistently at least $23\times$ faster. This acceleration factor will increase by several orders of magnitude for full-volume QMRI estimation problems involving more latent parameters per voxel.

Superconductivity has been the focus of enormous research effort since its discovery more than a century ago. Yet, some features of this unique phenomenon remain poorly understood; prime among these is the connection between superconductivity and chemical/structural properties of materials. To bridge the gap, several machine learning schemes are developed herein to model the critical temperatures ($T_{\mathrm{c}}$) of the 12,000+ known superconductors available via the SuperCon database. Materials are first divided into two classes based on their $T_{\mathrm{c}}$ values, above and below 10 K, and a classification model predicting this label is trained. The model uses coarse-grained features based only on the chemical compositions. It shows strong predictive power, with out-of-sample accuracy of about 92%. Separate regression models are developed to predict the values of $T_{\mathrm{c}}$ for cuprate, iron-based, and "low-$T_{\mathrm{c}}$" compounds. These models also demonstrate good performance, with learned predictors offering potential insights into the mechanisms behind superconductivity in different families of materials. To improve the accuracy and interpretability of these models, new features are incorporated using materials data from the AFLOW Online Repositories. Finally, the classification and regression models are combined into a single integrated pipeline and employed to search the entire Inorganic Crystallographic Structure Database (ICSD) for potential new superconductors. We identify more than 30 non-cuprate and non-iron-based oxides as candidate materials.

Inferring predictive maps between multiple input and multiple output variables or tasks has innumerable applications in data science. Multi-task learning attempts to learn the maps to several output tasks simultaneously with information sharing between them. We propose a novel multi-task learning framework for sparse linear regression, where a full task hierarchy is automatically inferred from the data, with the assumption that the task parameters follow a hierarchical tree structure. The leaves of the tree are the parameters for individual tasks, and the root is the global model that approximates all the tasks. We apply the proposed approach to develop and evaluate: (a) predictive models of plant traits using large-scale and automated remote sensing data, and (b) GWAS methodologies mapping such derived phenotypes in lieu of hand-measured traits. We demonstrate the superior performance of our approach compared to other methods, as well as the usefulness of discovering hierarchical groupings between tasks. Our results suggest that richer genetic mapping can indeed be obtained from the remote sensing data. In addition, our discovered groupings reveal interesting insights from a plant science perspective.

Uncertainty analysis in the form of probabilistic forecasting can significantly improve decision making processes in the smart power grid for better integrating renewable energy sources such as wind. Whereas point forecasting provides a single expected value, probabilistic forecasts provide more information in the form of quantiles, prediction intervals, or full predictive densities. This paper analyzes the effectiveness of a novel approach for nonparametric probabilistic forecasting of wind power that combines a smooth approximation of the pinball loss function with a neural network architecture and a weighting initialization scheme to prevent the quantile cross over problem. A numerical case study is conducted using publicly available wind data from the Global Energy Forecasting Competition 2014. Multiple quantiles are estimated to form 10%, to 90% prediction intervals which are evaluated using a quantile score and reliability measures. Benchmark models such as the persistence and climatology distributions, multiple quantile regression, and support vector quantile regression are used for comparison where results demonstrate the proposed approach leads to improved performance while preventing the problem of overlapping quantile estimates.

Data science and statistics are not magic. They won't magically fix all of a company's problems. However, they are useful tools to help companies make more accurate decisions and automate repetitive work and choices that teams need to make. Machine learning and data science get referenced a lot when referring to natural language processing, imaging recognition and chat bots. However, they also can be applied to help managers make decisions, predict future revenues, segment markets, produce better content and diagnosis patients more effectively. Below, we are going to discuss some case examples of statistics and applied data science algorithms that can help your business and team produce more accurate results. This doesn't require complex hadoop clusters and cloud analytics. Just, let's get the basics going first! Before we jump to far down the rabbit hole of technology and hype!

Regardless of whether the learner is a human or machine, the basic learning process is similar. Data storage utilizes observation, memory, and recall to provide a factual basis for further reasoning. Abstraction involves the translation of stored data into broader representations and concepts. Generalization uses abstracted data to create knowledge and inferences that drive action in new contexts. Evaluation provides a feedback mechanism to measure the utility of learned knowledge and inform potential improvements.

In today's era of big data, robust least-squares regression becomes a more challenging problem when considering the adversarial corruption along with explosive growth of datasets. Traditional robust methods can handle the noise but suffer from several challenges when applied in huge dataset including 1) computational infeasibility of handling an entire dataset at once, 2) existence of heterogeneously distributed corruption, and 3) difficulty in corruption estimation when data cannot be entirely loaded. This paper proposes online and distributed robust regression approaches, both of which can concurrently address all the above challenges. Specifically, the distributed algorithm optimizes the regression coefficients of each data block via heuristic hard thresholding and combines all the estimates in a distributed robust consolidation. Furthermore, an online version of the distributed algorithm is proposed to incrementally update the existing estimates with new incoming data. We also prove that our algorithms benefit from strong robustness guarantees in terms of regression coefficient recovery with a constant upper bound on the error of state-of-the-art batch methods. Extensive experiments on synthetic and real datasets demonstrate that our approaches are superior to those of existing methods in effectiveness, with competitive efficiency.